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From: scottw@advsysres.com  (Scott A. Whitmire)
Subject: Re: mathematics (algebra?) of object orientation
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References: <49c627$bgn@sparcserver.lrz-muenchen.de> <49d23s$6bk@Starbase.NeoSoft.COM> <MUSTO.95Nov28125302@hermes.informatik.unibw-muenchen.de> <4aph1c$sn6@nlrgup.nlr.nl>
Date: Fri, 15 Dec 1995 06:25:28 GMT
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Xref: glinda.oz.cs.cmu.edu comp.object:42844 comp.object.logic:639 comp.theory:14987 sci.math:129029

In <4aph1c$sn6@nlrgup.nlr.nl>, vyver@nlr.nl (vyver y.a.j.r. van de) writes:
>A class describes a set of objects. A subclass describes a
>subset of objects. The number of real persons (objects) in
>class Person is larger than the number of real persons in
>class employee (or could be equal if every person has
>an employer). So, although the number of attributes is larger,
>the actual number of objects described by these attributes
>becomes smaller. So a subclass describes (better not use 'is'
>because it may cause misunderstanding) a subset of the set
>described by the superclass.
>

Actually, a class is a *specification* for a set of objects. A class contains
a set of properties. It happens to be a set of properties shared by all of the
objects which are members of the class. (It is A set because an object could
be a member of more than one class, particularly when you take different
points of view into account). It is incorrect to say that the class itself is the
set of objects.

As an object in its own right, a class is a set of properties (attributes and
methods), and can be treated and operated on as a set.

>But, how would you define aggregation in terms of sets?

A class which contains, as an attribute, an object of another class is an
aggregation. The contained object is considered to be an attribute of the
container object.

Scott A. Whitmire             scottw@advsysres.com
Advanced Systems Research     
25238 127th Avenue SE         tel:(206)631-7868
Kent Washington 98031         fax:(206)630-2238

Consultants in object-oriented development and software metrics.

